Certain materials when struck by an incoming charged particle or ionizing radiation will “scintillate” or re-emit the absorbed energy in the form of light (i.e. photons). A scintillation-based detector can use a light sensor to absorb the light re-emitted from the scintillating material (i.e. the scintillator), producing electrical signals that provide specific information regarding the particle or ionizing radiation that struck the scintillator.
Scintillation-based detectors can be used in a variety of nuclear fuel cycle and homeland security applications. Some examples of systems where scintillation-based detectors are used include non-intrusive interrogation in portal and border monitors, content interrogation of shipping containers, nuclear material accountancy and nuclear safeguards verifications. Further examples of the capabilities and benefits of scintillation-based detectors include identifying contraband material while reducing the time required for such identification; providing rapid isotopic and spectroscopic information for non-destructive assay of dry cask storage systems for spent nuclear fuel; detecting weak radionuclide signals through the multi-purpose stainless steel canisters used for transportation and storage; determining breaches in nuclear fuel cladding; and identification of gamma (γ) emitting signatures in spent nuclear fuel facilities and reprocessing facilities as means of verification in the plutonium fuel cycle.
Furthermore, scintillation-based detectors can also be used in model medical imaging modalities as converters for x-rays and gamma (γ) radiation, thereby obtaining information about the interior of the body. Some examples of medical applications using scintillation-based detectors include x-ray imaging, computerized tomography, and positron emission tomography scanning systems.
Enhanced sensitivity of scintillation-based detectors can be accomplished by improving the energy resolution (ΔE) and timing resolution (Δt) of the detector. Optimal ΔE of a scintillation-based detector can be achieved with maximized photon yields and higher photoelectric cross sections (σpe) which result in higher probabilities of the scintillator capturing incoming radiation.
As σpe exhibits a generally proportional relationship to the effective atomic number (Zeff) of the scintillator, heavier and denser materials result in a higher number of photoelectrons (Npe) registered during the scintillation event. As a result, most of the scintillators used in scintillation-based detectors have high densities and high effective atomic numbers.
However, heavy materials generally exhibit high refractive indices (e.g. n1˜1.8-2.4) relative to the ambient medium, which is typically an air tight enclosure (n2=1) or grease (n2˜1.3). In such cases, the angle of total reflection (θtot) will be relatively small. Therefore, only a limited fraction, for example about 10 to 30 percent, of the re-emitted light is able to outcouple to the scintillator surface at which a photomultiplier tube (PMT) or other light sensor can be located. Further, total internal reflection in the scintillator material deteriorates the detector's sensitivity for low count events and increases the statistical spread of the collected photons.
The use of photonic crystal structures in association with the scintillators can allow for more efficient light extraction from the scintillator surface. In particular, photonic crystals can provide two-dimensional periodic patterns that increase the percentage of re-emitted light that is able to outcouple. For example, periodic diffraction gratings can inhibit the propagation of the emitted light along directions transverse and longitudinal to the surface, thereby creating a photonic band gap. Such an optical band gap can serve to minimize total internal reflection for light waves with incident angles (θi) larger than a total critical angle of total reflection (θtot).
As an example, FIG. 1 depicts enhanced light outcoupling provided by a photonic crystal scintillator 112. More particularly, scintillator 102 has a flat geometric structure at its interface with region 104 (e.g. air, grease, or vacuum). Therefore, light reemitted by scintillator 102 that approaches the interface at an incident angle larger than the total critical angle generally does not outcouple. On the other hand, photonic crystal scintillator 112 has a two-dimensional periodic pattern (e.g. repeating features such as 108 and 110) that increase the percentage of re-emitted light that is able to outcouple. In particular, light approaching at an incident angle larger than the total critical angle of scintillator 102 exhibits increased outcoupling and can therefore be observed by light sensor 106 (e.g. a photodiode, photomultiplier tube, or other light sensor).
Thus, redistribution of the saved energy can lead to enhanced light extraction from the patterned surface coupled to the light sensor. As an example, Monte Carlo simulations have shown that applying photonic structures to various scintillator materials can enhance light yields between 90 to 110 percent.
In some respects, a photonic band gap can be comparable to a semiconductor's electronic band gap arising from the interaction of the electron wavefunction with a crystalline periodic atomic lattice. In particular, Maxwell's equations can be applied to model the interaction of electromagnetic waves in photonic crystals. A more thorough derivation of these equations in a 2-D periodic dielectric media is described in J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, “Photonic Crystals: Molding the Flow of Light,” Princeton UP, 2008 and M. Skorobogatiy and J. Yang, “Fundamentals of Photonic Crystal Guiding,” Cambridge UP, 2009.
In this derivation, the third and fourth Maxwell equations are evaluated at a fixed frequency of propagation (ω) yielding an eigenfunction for the harmonic modes of the magnetic field component, as set forth in Equation 1 below:
                                          ∇            ->                    ⁢                      ×                          1              ɛ                        ⁢                                          ∇                ->                            ⁢                              ×                                  H                  ->                                                                    =                                            (                              ω                c                            )                        2                    ⁢                      H            ->                                              (                  Equation          ⁢                                          ⁢          1                )            
The corresponding solutions to this equation have the form of Equation 2 with eigenvalues ωn({right arrow over (k)}), where {right arrow over (H)}n,{right arrow over (k)} is a periodic envelope function satisfying Equation 3.
                                          H            ->                    (                      x            ->                    )                =                              ⅇ                          ⅈ              ⁢                                                          ⁢                                                k                  ->                                ·                                  x                  ->                                                              ⁢                                                    H                ->                                            n                ,                                  k                  ->                                                      (                          x              ->                        )                                              (                  Equation          ⁢                                          ⁢          2                )                                                      (                                                            ∇                  ->                                ⁢                                  +                  i                                            ⁢                                                          ⁢                              k                ->                                      )                    ×                      1            ɛ                    ⁢                      (                                                            ∇                  ->                                ⁢                                  +                  i                                            ⁢                                                          ⁢                              k                ->                                      )                    ×                                    H              ->                                      n              ,                              k                ->                                                    =                                            (                                                                    ω                    n                                    (                                      k                    ->                                    )                                c                            )                        2                    ⁢                                    H              ->                                      n              ,                              k                ->                                                                        (                  Equation          ⁢                                          ⁢          3                )            
In a photonic crystal structure, the dielectric constant (∈) is a function of position. For example, ∈({right arrow over (x)})=∈({right arrow over (x)}+Ri) where Ri are lattice vectors for an array in two dimensions. Thus, Equation 2 can result in a different eigensolution for each wave vector (k) of the primitive unit cell of the photonic crystal. Since the lattice structure is periodic, there will be discrete eigenvalues ωn({right arrow over (k)}) that are continuous functions of k and form bands when plotted as a dispersion relation or band diagram.
This periodicity further allows consideration of only the non-equivalent wave vectors close to the k=0 origin, which is called the first Brillouin zone of the dispersion relation. Further simplification leads to an irreducible Brillouin zone (ΓMKΓ) that is the smallest region in first Brillouin zone for which the eigensolutions are not related by symmetry.
A photonic band gap (PBG) is observed when Maxwell's equations are irresolvable over a range of ω for all k. Since electromagnetic fields have two types of polarization by symmetry (e.g. transverse magnetic (TM) and transverse electric (TE)), a photonic crystal may simultaneously exhibit a TM only band gap and a TE only band gap that do not overlap. However, a full band gap occurs when at least a portion of both the TM and TE band gaps overlap and propagation of both the electric and magnetic field components is prohibited.
As a rule of thumb, TE band gaps are favored in a connected vein lattice of high-∈ material, while TM band gaps are favored in a square lattice of isolated high-∈ regions. As an example, FIG. 2A depicts a connected vein lattice structure defined by regions having a low dielectric constant (e.g. 202) and connected veins (e.g. 204) having a high dielectric constant. TE band gaps are more prevalent in the photonic crystal structure depicted by FIG. 2A. As another example, FIG. 2B depicts a square lattice of high-∈ regions (e.g. 206) isolated within a general area having a low dielectric constant (e.g. 208). TM band gaps are more prevalent in the photonic crystal structure depicted by FIG. 2B
In order to design a photonic crystal that has band gaps for both TM and TE polarizations, a compromise can be made to obtain both isolated spots and connected veins of high dielectric constant material. As an example, FIG. 2C depicts one potential solution, which includes a honeycomb structure design of air columns (e.g. 210) within a high-∈ substrate (e.g. 212). If the radius of the columns is large enough, the spots (e.g. 214) between the columns can approximate localized regions of high-∈ material. Furthermore, the spots can be connected by veins (e.g. 216) through a narrow squeeze between the columns to adjacent spots. Thus, the band structure for the lattice depicted in FIG. 2C can result in a full photonic band gap for both the TE and TM polarizations.
However, a practical method for the fabrication of large-area photonic crystal scintillators has not been developed. In particular, the primary method of fabrication explored, e-beam lithography patterning, is time consuming, expensive, and is generally not scalable to manufacture large-area photonic crystal scintillators. In addition, only a few fabrication techniques are able to overcome the diffraction limit of light to produce features in nanometer and submicron scales.
Therefore, an effective, cost-efficient, scalable method of manufacturing photonic crystal scintillators is desirable.